Diffusion in glassy polymers. II

The Fickian diffusion coefficient of methylene chloride in a glassy epoxy polymer is calculated with the use of Crank's model of discontinuous change of D with concentration C. The diffusion constant is obtained as 1.93 × 10^?6 cm²/sec. The swollen layer behind the advancing solvent front is essentially in the rubbery state of the same polymer. The case II swelling by benzene is discussed in terms of a convective transport arising from the partial stress (internal) tensor of the penetrant. The superposition of Fickian and case II diffusion found with mixtures of methylene chloride and benzene is also discussed briefly.     

Mechanism of fracture in glassy polymers. IV. Temperature rise at the tip of propagating crack in poly(methyl methacrylate)

The temperature rise at the moving crack tip in poly(methyl methacrylate), resulting from the dissipation of the energy of crack propagation has been calculated. At velocities below 1 cm./sec., conduction of heat away from the crack plane into the bulk polymer appears to prevent any appreciable temperature increase.     

Craze initiation of glassy polymers under the action of crazing agent

This paper deals with the formation of crazes that may be caused by an external load on glassy polymers wetted with kerosene. First, the orientation of crazes has been determined when applying a uniaxial tension to a specimen of cold-rolled polyvinyl chloride sheet at various angles to the rolling direction. The critical stress for craze initiation in poly(methyl methacrylate) and polyvinyl chloride rods has been investigated under combined tension–torsion loading. It is shown that: (1) in an anisotropic, as well as an isotropic polymer, the direction of crazes is perpendicular to that of the maximum strain calculated by taking into account the internal stress due to rolling; and (2) under the action of a crazing agent, crazing may occur even under the pure torsional load, i.e., in the absence of dilatational stress.     

Micromechanics of fatigue crack propagation in glassy thermoplastics

By the aid of the optical interference method the size of the craze zone at the crack tip has been measured during fatigue crack propagation (FCP) in two glassy thermoplastics thus giving a basis to re-examine proposed models. In contrast to previous assumptions it has been found, that in PMMA of high molecular weight crack propagation occurs only during a short interval of the loading cycle when the fibrils are stretched most severely and it is not limited by crack tip blunting; between the dimensions of the craze zone and the crack advance per cycle which is also reflected by markings on the fracture surface no simple correlation has been found. In PVC first the craze grows continuously during many loading cycles up to its final size and then the crack propagates by a jump separating the craze zone only partly. Thus at all stress intensity levels investigated the length of the final craze zone has been found to be distinctly larger than the jump spacing on the fracture surface. By aid of SEM-photography it is shown that in PVC during FCP cracking occurs by separation of fibrils instead of void coalescence.     

Theoretical models for diffusion in glassy polymers. II

The author refines and generalizes a model for diffusion in glassy polymers which he previously introduced. The model unifies many diverse observations by explicity formulating the common property of a glassy polymer in all its various modes, namely the finite relaxation time due to its slow response to changing conditions. An integral approximation method is used to study the motion of the penetrant front and the glass-gel interface and a useful polynomial approximation method is introduced for use in special simple situations.     

Mechanism of fracture in glassy polymers. III. Direct observation of the craze ahead of the propagating crack in poly(methyl methacrylate) and polystyrene

Observation of optical interference fringes at the tip of a crack in a glassy polymer allows the construction of the configurations of the crack tip and the craze that precedes it. The craze extends 25 μ beyond the crack tip in poly(methyl methacrylate) and 550 μ beyond the tip in the polystyrene studied. The craze at the crack tip in PMMA may be seen to deform elastically as much as 100% under stress before crack propagation recommences. Such deformation is estimated to account for as much as 40% of the nominal Griffith energy of crack propagation.     

Mechanisms and micromechanics of fatigue crack propagation in glassy thermoplastics

An iterative approach is used to estimate, from interference optics measurements, the variation of refractive index and, hence, extension ratio along the length of a craze at the tip of a fatigue crack. The finite element method is used to compute craze surface stress distributions which are found to be similar to those obtained for static loading. High extension ratios, in the range 6 to 8 for retarded fatigue crack growth in poly(vinylchloride), are attained in the craze fibrils at the crack tip before crack jump occurs. The craze thickens primarily by surface drawing during the early stages of its growth but in the later stages the fibril creep mechanism predominates. The critical fibril extension ratio is not reached in a single cycle, as in normal fatigue crack propagation, and crack jump does not occur until, typically, after several hundreds of cycles during which the fibrils accumulate considerable damage.Presented in part at the 7th Int. Conference Deformation, Yield and Fracture of Polymers, Cambridge, UK, 11–14 April 1988.     

A scaling analysis of the fracture mechanisms in glassy polymers

Recent experimental work on craze growth in polymers has shown that the reptation model for polymer motion may be successfully applied, in certain cases, to the behavior of glassy polymers in the solid phase. In this paper, a simple scaling analysis is presented to show how the primitive path model for reptation may be applied to the behavior of glassy polymers before and during slow crack growth. Different dynamic regimes are identified and related to the relaxation times of the polymer chain. The dependence on polymer chain length for each mechanism is described. Estimates for the fracture energy of each process are presented.     

Cyclic crack propagation and molecular kinetics of polymers

Cyclic tests in tension were performed on PMMA and PC center-notched plate specimens. Frequencies between 0.1 and 100 Hz at temperatures from ?78 to +55°C were investigated. Correlations between crack growth rates, described in the terms of stress intensity K, and the appropriate values of the loss factor tan δ were studied. It was concluded that, in the investigated conditions, a direct correspondence exists between the crack growth rate and tan δ.     

Nonequilibrium statistical theory of damage and fracture for glassy polymers, 1. The statistical distribution and evolution of microcracks in glassy polymers

The purpose of this paper is to construct a unified theoretical framework to link micro to macro-mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso-mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any-order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first-order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.     

Energy-consuming micromechanisms in the fracture of glassy polymers. I. Chain scission in polystyrene

The number of chain scissions per unit area that occur during the fracture of partially annealed latex films from M_n ? 180,000 g/mol polystyrene particles of about 275 Å radius were measured and correlated to annealing times. A curve with four regimes was found. At short annealing times the curve is nearly flat, in what is called the chain pull-out regime. In the second regime, the number of chains broken per unit area increases with a 0.8 power of annealing time as entanglement of the diffusing polymer chains increases in neighboring host particles. This is in good agreement with Wool's theory which predicts a 0.75 power dependence. Then, after reaching a peak, the number of scissions decreases in the third regime, indicating a change in fracture mechanism. The number of chain scissions increases again in the fourth regime, as final healing of the film interface takes place. Fracture surface analysis reveals a rough surface for short annealing times and a smooth surface for longer annealing times. The number of polymer chain scissions per unit area of fracture surface showed no dependence on initial molecular weights for t ? τ_r where t and τ_r are annealing and relaxation times, respectively. The number of chain bridges crossing a unit area of interface was suggested as the basic molecular property. © 1992 John Wiley & Sons, Inc.     

Diffusion in glassy polymers. I

Synopsis The diffusion of six solvents in three crosslinked, glassy epoxy polymers is studied. Case II swelling and Fickian sorption are observed as two simple limiting cases. The mechanism of diffusion changes from one limit to another as the nature of the solvent or the crosslink density of the polymer is altered. With mixed solvents, properly chosen, a superposition of Fickian diffusion and case II swelling is observed.     

Diffusion in glassy polymers. III

The diffusion studies of several solvents in epoxy polymer reported by Kewi and Zupko in Part I of this series are explained with the solution obtained from the generalized diffusion equation which includes the internal stress contribution. The rate of permeation of a penetrant through a polymer film and the time lag needed to reach steady state are also given for the generalized diffusion equation.     

Heating of polymers during neck propagation

The heating of polyethylene terephthalate, polyamide-66, and polyamide-6 during tensile drawing at room temperature was studied theoretically and experimentally. At a low draw rate, the necking temperature was close to the temperature of the surrounding air. An increase in the rate results in the transition to the adiabatic conditions of drawing. A necking temperature of 140°C was experimentally recorded in polyethylene terephthalate at a draw rate of 1000 mm/min and during the approach to the adiabatic conditions of drawing. A formula describing the dependence of the necking temperature on the draw rate was derived. The resulting value agreed fairly well with the theoretical estimation of the temperature. The drawing (strain) ratio in the neck and the draw stress are the crucial parameters determining the temperature. The rate of the transition to the adiabatic conditions of drawing was determined. The temperatures of adiabatic heating for various polymers were calculated. The increases in the temperatures of polycarbonate and low- and high-density polyethylene are relatively low. The increases in temperature can be regarded as moderate for polypropylene and polyvinyl chloride, while they attain the highest values in polyamide-6 and polyethylene terephthalate owing to the high draw ratios in the neck and the high draw-stress values.     

The influence of temperature and frequency on fatigue crack propagation in polymers

Summary Centrally notched plate specimens of PMMA and PC were cycled in tension between constant stress intensity limits and crack growth was monitored against the number of cycles. A range of frequencies between 0.1 IIz and 100 Hz, and of temperatures between – 70 °C and + 40 °C was investigated. It was found that the cyclic crack growth decreased with decreasing temperature and/or increasing frequency. A linear relationship between crack length and number of cycles was observed. Application of the cyclic crack propagation law proposed byArad-Radon-Culver, namelyd(2a)/dN = ⁿ where is (K _max ² -K _min ²) and K_max andK _min are the respective values of maximum and minimum stress intensity factors, indicates that the indexn is unaffected by temperature or frequency variations in the investigated range (II regime of fatigue crack propagation) and the law would be a valid model if the term is suitably determined.

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Zusammenfassung Ermüdungsversuche im Rahmen der linearelastischen Bruchtheorien wurden ausgeführt auf zentralgekerbten Platten von PMMA und PC, sowie Rißwachstum als Funktion der Belastungszahl gemessen. Frequenzen von 0.1 Hz bis 100 Hz und Temperaturen von – 70 °C bis 40 °C zeigten, daß sich das Rißwachs-tum mit verringerter Temperatur und/oder erhöhter Frequenz verringerte. Eine lineare Abhängigkeit der Rißlänge von Belastungszahl wurde festgestellt. Die Benutzung der Rißausbreitung-Analyse von Arad-Radon-Culverd(2a)/dN =ⁿ, wo ist (K _max ² -K _min ²), zeigt, daß der Indexn nicht beeinflußt ist von Temperatur oder Frequenzwechsel in dem untersuchten Bereich (das sogenannte zweite Regime des Ermüdungswachstums). Wenn man die Konstante festgestellt hat, dann ist die Arad-Radon-Culver-Methode direkt benutzbar.

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With 12 figures     

Intrinsic crazing and anisotropy of maximum recoverable extension in oriented glassy polycarbonate

The critical draw ratio for initiation of intrinsic crazing in polycarbonate below the glass transition temperature has been determined after preorientation in the melt. Even when referred to the isotropic state, this ratio is found to depend not only on the extent of preorientation but also to be distinctly anisotropic. Under the assumption that intrinsic crazing occurs at the maximum extension of the entanglement network, these results are incompatible with a strain dependent but homogeneous breakdown of the entanglement network, but can be interpreted in terms of departure from affine transformation of the radius of gyration of an entangled length.     

Properties of fracture surfaces of glassy polymers: Chain scission versus chain pullout

Fresh fracture surfaces formed by tensile failure of craze in molded polystyrene (PS) bars have been compared with the molded surfaces of the same bars, using an atomic force microscope with a thermal probe and operated in local thermal analysis. The results indicate that molecular weight is much higher in the interior of the sample than at the surface. No evidence was found for degradation of the PS chains via chain scission during crazing. Alternative explanations for the low‐molecular weights at the molded surface are discussed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Effects of polar group incorporation on crazing of glassy polymers: Styrene–acrylonitrile copolymer and a dicyano bisphenol polycarbonate

The degree of swelling and attendant reduction in the glass transition temperature have been determined for a 70% styrene–30% acrylonitrile copolymer in a large number of organic liquids. The critical strain ?_c for crazing or cracking has been determined also in air and in each agent. Limited crazing data have been obtained also on a dicyano bisphenol polycarbonate in which the CN groups take the place of the methyl groups in bisphenol A (BPA) polycarbonate. The two resins are compared with polystyrene and BPA polycarbonate, respectively, in terms of crazing resistance, swelling, and other properties. In both systems CN incorporation raises ?_c (air) and reduces susceptibility to liquids of low solubility parameter δ; T_g and shear yield stress are raised in the polycarbonate but not in the styrene system. The volume efficiency of CN in raising ?_c (air) is greater in the polycarbonate system than the styrene system; for the rise in polymer solubility parameter, CN efficiency is apparently reversed. These changes are discussed in terms of the differences in molecular architecture of the two systems. For glassy polymers, ?_c (air) is shown to depend in semiquantitative fashion on polymer T_g, δ, and resistance to shear deformation.     

Concentration-dependent transport of gases and vapors in glassy polymers: II. Organic vapors in ethyl cellulose

The solution (sorption) and transport of acetone, benzene, and methanol vapors in ethyl cellulose have been studied by Barrer, Barrie and Slater [5, 6] over a range of temperatures and penetrant concentrations. The solubility isotherms for the three penetrants as well as the diffusivity and permeability data for acetone reported by these investigators are analyzed in terms of a “dual-sorption” model with partial penetrant immobilization [3], assuming that the diffusion coefficient is concentration dependent [4].